Do you think the limit of the map as its error goes to zero exists? Do you think we will ever be able to determine whether or not the limit exists? What name would you give that limit if it existed?

The equivalent language I prefer is more lay-person: will science ever explain everything we observe and predict everything we may ever observe? And my answer is: there is no way to tell at this point, and the answer[ability] is not relevant to anything we do. After a moment of thought you can see that this might not even be the right question to ask: some day we might be powerful enough and smart enough to create new physical laws, so even defining such a limit will be meaningless.